Conţinutul numărului revistei 
Articolul precedent 
Articolul urmator 
805 4 
Ultima descărcare din IBN: 20210925 16:21 
SM ISO690:2012 SCHLOMIUK, Dana; VULPE, Nicolae. Integrals and phase portraits of planar quadratic differential systems with invariant lines of total multiplicity four. In: Buletinul Academiei de Ştiinţe a Moldovei. Matematica. 2008, nr. 1(56), pp. 2783. ISSN 10247696. 
EXPORT metadate: Google Scholar Crossref CERIF DataCite Dublin Core 
Buletinul Academiei de Ştiinţe a Moldovei. Matematica  
Numărul 1(56) / 2008 / ISSN 10247696  


Pag. 2783  


Descarcă PDF  
Rezumat  
In this article we consider the class QSL4 of all real quadratic differential systems
dx dt = p (x, y), dy dt = q(x, y) with gcd(p, q) = 1, having invariant lines of total
multiplicity four and a finite set of singularities at infinity. We first prove that all
the systems in this class are integrable having integrating factors which are Darboux
functions and we determine their first integrals. We also construct all the phase
portraits for the systems belonging to this class. The group of affine transformations
and homotheties on the time axis acts on this class. OurMain Theorem gives necessary and sufficient conditions, stated in terms of the twelve coefficients of the systems, for the realization of each one of the total of 69 topologically distinct phase portraits found in this class. We prove that these conditions are invariant under the group action. 

Cuvintecheie quadratic differential system, affine invariant polynomial, configuration of invariant lines, Poincar´e compactification, algebraic invariant curve 

